Question: Rewrite as a simplified fraction. ${2.4\overline{90} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2490.909...\\ 10x &= 24.909...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2466}$ ${x = \dfrac{2466}{990}} $ ${x = \dfrac{137}{55}} \text{or} {2 \dfrac{27}{55}}$